In 1854 he became a lecturer at the University of Bonn, and during the following year was appointed professor of German legal history and canon law at the University of Prague. In 1873 he returned to Bonn, where he was a professor of canon law until 1906. In 1881-82 he was rector at the university.

Schulte opposed the First Vatican Council, and was architect of the basic templates regarding church law for organization of the German Old Catholic Church. He was also author of the Synodal- und Gemeindeordnung (Synodal and Municipal Order) of 1874, the fundamental law of the Old Catholic Church in Germany. From 1871 to 1890 he was president of the Old Catholic Congress.

Die Geschichte der Quellen und Literatur des Kanonischen Rechts von Gratian bis auf die Gegenwart (The History of Literature and Sources of Canon Law of Gratian up to the Present) (1875-1880, four volumes)